We develop an inflationary model without small parameters on the basis of
    multidimensional $f(R)$ gravity with a minimally coupled scalar field. The
    model is described by two stages of space expansion. The first one begins at
    energy scales about the D-dimensional Planck mass and ends with the de Sitter
    metric of our space and the maximally symmetric extra dimensions. In the
    following, the quantum fluctuations produce a wide set of inhomogeneous extra
    metrics in causally disconnected regions quickly generated in the de Sitter
    space. We find a specific extra space metric that leads to the effective
    Starobinsky model that fits the observational data.

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